Many people have thought about winning easy money, and the most suitable way to do this is to play the lottery. In Brazil, who controls lottery-related products is Caixa, a financial institution of the Federal Government. Among the most famous and that pays millionaire prizes is Mega Sena, but there are other products such as lottomania, lotca, quina, easy lotto, among others.
The easy lotto is considered by players to be one of the easiest to bet and win. It consists of a card of 25 numbers (01 to 25) among which we have marked 15 numbers. Prizes are paid to whoever hits 11, 12, 13, 14 or 15 tens. The chances of winning the lotto mania are as follows:
To carry out the calculations we will use factorial fundamentals of a number and combination of numbers.
Factorial: multiplication of all natural predecessors of a number.
4! = 4*3*2*1 = 24
Combination: subsets of n elements taken k to k, from the given set.
Formula:
hitting 15 numbers
We have a combination of 25 numbers taken from 15 to 15.
hitting 14 numbers
We have the following possibilities:
15 elements of which we must guess 14 and there are still 10 elements of which there is one that was not drawn.
hitting 13 numbers
We have:
15 elements of which we must guess 13 and there are still 10 elements of which there are two that were not drawn.
hitting 12 numbers
We have:
15 elements of which we must guess 12 and there are still 10 elements of which there are three that were not drawn.
hitting 11 numbers
We have:
15 elements of which we must guess 11 and there are still 10 elements of which there are four that were not drawn.
by Mark Noah
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/matematica/probabilidade-na-loto-facil.htm